Weide, Reinder van der (2022) The knot complement and its homotopy. Bachelor's Thesis, Mathematics.
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Abstract
We study the knot complement as topological space. First, the existence of Seifert surface is proven and their fundamental group is computed. Secondly, the cyclic coverings of the knot complement are constructed. Then, fibre bundles are introduced and used to define fibred knots, of which the commutator subgroup of the fundamental group can be computed. To finish off, we present a topological space that is homotopy-equivalent to the knot complement. By explicitly constructing the infinite cyclic cover of this space, the first homology group of the infinite cyclic covering of the knot complement is computed.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Veen, R.I. van der and Seri, M. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 22 Jul 2022 07:54 |
| Last Modified: | 22 Jul 2022 07:54 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/27862 |
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